Abstract:Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually unintelligible interior coordinates. One matrix multiplication per model pair removes it: an orthogonal Procrustes fit on a single batch of activations transfers sparse-autoencoder feature dictionaries and steering vectors between independently trained models, with no retraining.
The phenomenon is invisible to the standard SAE universality metric. Decoder-column cosine similarity matches across seeds at 98%, the SAE-universality headline number, while an SAE trained on one seed reconstructs another seed's activations at negative explained variance, worse than predicting the constant mean. The decoder columns align; the encoder reads from a rotated frame. A single Procrustes rotation $R$ restores reconstruction to within 0.025 EV of the within-seed ceiling at every internal site.
$R$ is Haar-distributed: $\|R - I\|_F$ matches the random-orthogonal prediction $\sqrt{2 d_{\mathrm{model}}}$ to 0.1% at $d_{\mathrm{model}} = 512$, and a Kolmogorov-Smirnov test of $R$'s eigenvalue spectrum against Haar $\mathrm{SO}(d_{\mathrm{model}})$ returns $p \approx 1.000$ pooled and per-pair. Diff-of-means steering vectors transfer in three regimes by alignment with $R$'s invariant subspace: clean when pinned by shared output weights, partial when overlapping the rotated subspace, inverted otherwise. With no shared I/O (Pythia), all three collapse to universally inverted. The same rotation account holds across training checkpoints within a single run.
Validated on a 104k-parameter Dyck-3 transformer and nine independently-trained Pythia-70m seeds on The Pile, via a pre-registered four-bar operational framework. Frontier-scale (10B+) replication remains open.
| Comments: | 26 pages, 4 figures, 40 references. Pre-registered four-bar framework; all numerical claims reproducible |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| ACM classes: | I.2.6; I.2.7 |
| Cite as: | arXiv:2605.24577 [cs.LG] |
| (or arXiv:2605.24577v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24577 arXiv-issued DOI via DataCite (pending registration) |
From: Jordan McCann [view email]
[v1]
Sat, 23 May 2026 13:37:59 UTC (66 KB)
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